The present invention relates to a method and an apparatus for dividing a shape expressed on a three-dimensional space into a large number of elements. More specifically, the present invention relates to a method for capable of easily generating a finite element mesh with less distortion in an original shape model and of controlling coarse/fine characteristics of this finite element mesh without correcting the original shape model and without newly producing an auxiliary line and an auxiliary point with regard to the original shape model in the mesh generating method of the finite element model for the finite element method, and also to an apparatus into which this mesh generating method is applied.
Conventionally, there are such methods that to analyze a numeric simulation for a phenomenon in a high efficiency, a finite element mesh is produced on a shape model to be analyzed by employing the mapping method, and thus calculation precision as well as calculation efficiencies can be improved. As such a method, automatic mesh generating methods have been proposed as described in H. TAKAHASHI, et al, "A Three-Dimensional Automatic Mesh Generation System Using Shape Recognition Technique", Transactions of the Japan Society of Mechanical Engineers, Vol. 59, No. 560, April 1993, pages 279 to 285, JP-A-1-311373 and JP-A-2-236677. They are realized in, for example, the combination type mechanical system CAE (Computer Aided Engineering) system HICAD/MESH.
As a finite element mesh producing method with employment of the mapping method, there is such a method that a mesh unnecessary to a user is deleted from the pattern of a mapping model prepared by the system, to easily produce a mapping model applied to the shape model, so that calculation precision and calculation efficiency are improved. As such a method, there is a semi-automatic mesh generating method as disclosed in JP-A-5-2627.
In a conventional automatic mesh generating techniques, only an original shape model and a finite element mesh generating model as the final result are displayed on a display screen. As a consequence, a user of the system could not acquire intermediate information by intervening in a mesh generating stage. Even when the above-explained semi-automatic mesh generating method is employed, there is a limitation in applicable shapes.
On the other hand, in connection with complex matters of an original shape model, there is such a case no determination can be made as to a direction in which each line segment is to be mapped in the course of mapping onto orthogonal coordinates space, which course is a part of internal processing in the system, in order not to establish contradictory conditions with the shape model. As a result, a recognition model could not be produced, and even when a mesh is produced, the mesh may contain a very distorted element. There is another case where a mesh different from user's requirements of the system use is produced in accordance with an automatically determined mapping direction.
In the conventional system, when an intermediate model couldn't be generated, an error message is displayed on the screen to interrupt the processing. As a result, the system user has to return to the initial condition and then correct a part which caused the error in the shape model based on his experiences. Thereafter, the user either starts the mesh producing processing, or accepts the mesh generated by the system.
Even when the system user wants to correct distorted elements in a generated mesh, the user has to return to the initial condition of the mesh generating processing, in which the shape model and the division number must be modified. In accordance with the above-described method, the more the shape of a model becomes complex, the more lengthy processing time and cumbersome processing are required. On the other hand, there is another method such that some patterns of the mapping model are previously prepared and a pattern thereamong is modified in a semi-automatic manner on an element basis so as to conform to the shape model. However, such a method could not be applied to complex shape models.
As one method for solving these problems to easily and surely produce a mesh, there is a need to introduce such an interactive user intervening method by a user in order that problems occurred at a mesh producing stage during an automatic processing can be solved, and the system user can produce his desirable mesh without modifying the shape model.